Adding a cog going from 7 to 8 speed cassette between a couple gears that are spaced to wide isn’t half step. Half step is having two chain rings close in size so that for any given cog on the cassette the ratio is half way between it and the next cog when shifting between rings. Half step plus granny is just adding a bailout range. In the old days with “10 speed” bikes 2X5 the steps in the back were pretty big and the desire for a half way between gear was great. In today’s world with 3X10 and such with tightly spaced cassettes there is little desire for half way between gears. In fact on the touring forum there is lots of talk about running 1X10 gearing as it simplifies the bike with the strong riders that tour ultra-light. If I lived in a flat part of the world I could easily see running a 1X setup.

The OP mentioned the desire to have a middle ring that is centered on the cassette allowing use of all the cogs. Any middle gear would work if you can find a cassette with tooth counts that work with their abilities. 11t is the starting tooth and the smallest you can find and if they seldom go past the 15t cog off the 38t ring the best 8 speed they could do would be a 11,12,13,14,15,16,17,18 if there is even such a thing in a compact cassette. The down side is the granny range goes way up.

Because the cassette is one thing to the two road rings and another thing to the Granny ring it’s always going to be some kind of compromise. One method they came up with is the mega-range cassette where the cogs are tightly spaced except the largest one and it’s huge in comparison. The idea is you just get one bailout granny combination to get you up any hill. Many people like a setup like this. I didn’t care for it because there are times that gear was so low it wasn’t needed you are looking at 3 or 4 MPH spinning as fast as you can and the next step was too high for the climb. But it is a good method of getting a tight cluster and still have a climbing cog like a 32t or a 36t.

Road bike riders and racers are very sensitive to slight changes in gearing and the thing that compromises when they can’t find their perfect gear is their cadence has to adjust and they are very sensitive to max output due to cadence change. For most of us say spinning 100RPM and changing a gear and having to do 95RPM that 5% change isn’t noticed too much. And if we are willing to give up some precision for a wider spacing between cogs to have a bigger inclusive range that’s what we do. I’m not proposing people worry about half step gearing just that if you have a wide spaced cassette and a triple the big ring really only gives you one or two more gears and in lots of cases such as the op they are getting too tall to be useful.

So you have a couple choices pick two rings that split the range like mtn cranks do, or get a center ring that works with all the cassette and keep the big ring for what it’s worth a high gear or two. I picked option 3 where the big ring gave me just one more gear within my useful range and all the rest of them half way between the middle rings, and a straight chain line on my tall gears.

I only posted in because it sounded like the OP was thinking down that road.